Greg and Tina read books. Greg has read 10 books and reads 5 more each week. Tina has read 5 books and reads 5 more each week. After how many weeks will they have read the same number of books?

Question

Write an equation that represents the number of books Tina has read, y, after x weeks.
Nice!
Complete the table below with the number of books, y, that Tina has read after 2, 4, and 8 weeks. You can solve on paper and then enter your answer on Zearn.
y=5+5x

Weeks (x) Books (y)
2
4
8
Great job!
Next, graph the points you just found on the coordinate plane to show the relationship between x, the number of weeks, and y, the number of books Tina has read.
Weeks (x) Books (y)
2 15
4 25
8 45
Excellent!
Now, consider Greg. Write an equation that represents the number of comic books Greg has read, y, after x weeks.

Answer 1

To represent the number of books that Greg has read after \( x \) weeks, we can write a similar equation to the one for Tina.

Greg has already read 10 books and reads 5 more each week. Therefore, the equation for the number of books Greg has read, \( y \), after \( x \) weeks can be written as:

\[ y = 10 + 5x \]

Now you have both equations:

• For Tina: \( y = 5 + 5x \)
• For Greg: \( y = 10 + 5x \)

To find out after how many weeks they will have read the same number of books, you can set the two equations equal to each other:

\[ 5 + 5x = 10 + 5x \]

Solving this equation will show the number of weeks needed for Greg and Tina to have read the same number of books. Simplifying gives:

\[ 5 + 5x - 5x = 10 \] \[ 5 = 10 \]

This is incorrect, meaning we must consider further coordination. In this case, since they both read at the same rate of 5 books per week, we can see they will never read the same total number because Greg starts with more books.

Thus, they will only read the same number of new books in the same weeks, but their total will differ since Greg started higher.

If you need to graph their equations or calculate additional values, please let me know!